1996 Jaguar Vanden Plas mystry stalling

My jag has developed a stalliing problem that no one seems to be able to diagnose. It does not do it all the time - so when I take it in to my mechanic - of course it does not happen when they drive it! I take it to a jag (only) mechanic who has been working on jags for 25 years - and he is as frustrated as I am with not being able to figure this out.
Here is what is happening;
car will be running fine and I will come up to a stop light and stop - keep my foot on the brake - and when it is time to go - step on the gas - engine does a "light" shudder and goes dead - I put it in park and it re-starts with no problem. One time I was making a slow u-turn on residential street and during the turning process it stalled out. One time I was coming out of a shopping mall - came to the stop sign - waited to enter the street and it stalled when I steppen on the gas.

My mechanic has already removed the throttle body for cleaning and replaced idle control valves. They have taken it to the dealer to hook up to computer and nothing shows as a problem. I put only Cheveron Supreme gas in it.

It scares me to death though because I never know when it will happen - and at stop lights it is very dangerous as it looks like I am ready to move to the person behind me - and then the car stalls out and I have to stop - put in park and restart - so I am almost getting hit from behind each time.

I prey that you have some good suggestions for me to explore with my mechanic as I am scared to death by this mystry stalling.

Thanks so much for any suggestions. Sorry - I am retired and out of money.